Constrained Max Drawdown: a Fast and Robust Portfolio Optimization Approach

ArXiv ID: 2401.02601 “View on arXiv”

Authors: Unknown

Abstract

We propose an alternative linearization to the classical Markowitz quadratic portfolio optimization model, based on maximum drawdown. This model, which minimizes maximum portfolio drawdown, is particularly appealing during times of financial distress, like during the COVID-19 pandemic. In addition, we will present a Mixed-Integer Linear Programming variation of our new model that, based on our out-of-sample results and sensitivity analysis, delivers a more profitable and robust solution with a 200 times faster solving time compared to the standard Markowitz quadratic formulation.

Keywords: Maximum Drawdown, Mixed-Integer Linear Programming (MILP), Portfolio Optimization, Markowitz Model, Risk Management, Portfolio Management

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 5.0/10
• Quadrant: Lab Rats
• Why: The paper introduces a novel linearization of the Markowitz model using maximum drawdown, involving advanced optimization techniques like Mixed-Integer Linear Programming (MILP) and sensitivity analysis, which increases math complexity. However, while it reports out-of-sample results and performance metrics, the excerpt lacks detailed implementation code, specific datasets, or extensive statistical validation, keeping empirical rigor moderate.

  flowchart TD
    A["Research Goal: Robust & Fast Portfolio Optimization"] --> B[""Methodology: MILP Formulation
    (Constrained Max Drawdown)""]
    B --> C[""Data/Inputs: Historical Returns
    (e.g., COVID-19 Period)""]
    C --> D["Computational Process: MILP Solver"]
    D --> E["Key Outcomes: <br>1. 200x Faster Solving Time <br>2. More Profitable & Robust Results"]
    E --> F["Comparison: Outperforms Standard Markowitz"]